Question

Does \(\left[\mathrm{OH}^{-}\right]\) remain constant in all aqueous solutions? Why or why not?

Short answer

No, \\([ ext{OH}^-]\\) does not remain constant as it adjusts to changes in neutralization constant \(K_w\) when acids or bases are added.

Step-by-step solution

Understanding the Nature of Aqueous Solutions

Aqueous solutions contain water as the solvent. Water can ionize to a small extent, forming hydronium (\( ext{H}_3 ext{O}^+\) or simply \( ext{H}^+\)) and hydroxide ions (\( ext{OH}^-\)). This is represented by the equilibrium \( ext{H}_2 ext{O} ightleftharpoons \text{H}^+ + \text{OH}^-\).

Equilibrium Constant for Water Ionization

For the ionization of water, there is an equilibrium constant, \(K_w\), which is equal to the product of the concentrations of \( ext{H}^+\) and \( ext{OH}^-\), where \(K_w = [ ext{H}^+][ ext{OH}^-]=1.0 \times 10^{-14}\) at 25°C. This implies that the concentration of \( ext{OH}^-\) changes with \([ ext{H}^+]\).

Effect of Adding Acids or Bases

When an acid is added to the solution, \([ ext{H}^+]\) increases, causing \([ ext{OH}^-]\) to decrease to maintain the constant value of \(K_w\). Conversely, when a base is added, \([ ext{OH}^-]\) increases, which means \([ ext{H}^+]\) decreases.

Conclusion about \([ ext{OH}^-]\) in Aqueous Solutions

Since the addition of other substances alters \([ ext{H}^+]\), which in turn affects \([ ext{OH}^-]\) to maintain the equilibrium constant \(K_w\), the concentration of \([ ext{OH}^-]\) cannot remain constant in all aqueous solutions.

Key concepts

Water Ionization

Water ionization is a fascinating process where water molecules spontaneously dissociate into ions. In an aqueous solution, which includes water as the solvent, countless molecules are moving and interacting. Some of these molecules, specifically water (H_2O), can break apart to form ions. This process is known as water ionization.

During ionization, water molecules split into two types of ions:

• Hydronium ions (H_3O^+) or simply hydrogen ions (H^+)
• Hydroxide ions (OH^-)

This equilibrium reaction can be represented by the formula:\[H_2O \rightleftharpoons H^+ + OH^-\]
In pure water at 25°C, the concentrations of hydronium and hydroxide ions are both 1.0 \times 10^{-7} M. But the concentrations can change depending on what is added to the water, such as acids or bases.

Hydroxide Ion Concentration

In any aqueous solution, the concentration of hydroxide ions ( OH^- ) is an important factor in determining the solution's properties. Remember, hydroxide ions form when water ionizes. However, their concentration can vary significantly when the solution is altered with other substances like acids and bases.

• Adding an acid: This will increase the concentration of hydronium ions ( H^+ ), and since the product of [ H^+ ][ OH^- ] must remain constant (thanks to the equilibrium constant K_w ), the concentration of hydroxide ions must decrease.
• Adding a base: This increases [ OH^- ], so the concentration of hydronium ions ( H^+ ) must decrease to maintain K_w .

Because of this dynamic, the [ OH^- ] doesn't stay constant in aqueous solutions where other substances are present, changing the acid-base balance.

Equilibrium Constant

The equilibrium constant is a crucial concept in understanding how reactions proceed in aqueous solutions. For water ionization, the equilibrium constant is denoted as K_w. At 25°C, K_w value is 1.0 \times 10^{-14}. This equation is expressed as:\[K_w = [H^+][OH^-]\]
This means that the product of the concentrations of hydrogen ions and hydroxide ions in a solution is always the same, at given conditions.

The equilibrium constant helps us understand why hydroxide concentrations change when substances are added to a solution:

• If [H^+] increases, such as when an acid is added, [OH^-] must decrease to keep K_w constant.
• On the other hand, if a base is added, boosting [OH^-], the concentration of [H^+] should drop to maintain iK_w.

Hence, K_w is central to predicting and explaining changes in ion concentrations in water, making it clear that [OH^-] cannot remain constant amidst these changes.